Quickly-Decodable Group Testing with Fewer Tests: Price-Scarlett's Nonadaptive Splitting with Explicit Scalars.
ISIT(2023)
摘要
We modify Price and Scarlett’s fast binary splitting approach to nonadaptive group testing [1]. We show that, to identify a uniformly random subset of k infected persons among a population of n, it takes only ln(2−4ε)
−2
k ln n tests and decoding complexity O(ε
−2
k ln n), for any small ε > 0, with vanishing error probability. In works prior to ours, only two types of group testing schemes exist. Those that use ln(2)
−2
k ln n or fewer tests require linear-in-n complexity, sometimes even polynomial in n; those that enjoy sub-n complexity employ O(k ln n) tests, where the big-O scalar is implicit, presumably greater than ln(2)
−2
. We almost achieve the best of both worlds, namely, the almost-ln(2)
−2
scalar and the sub-n decoding complexity. How much further one can reduce the scalar ln(2)
−2
remains an open problem.
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关键词
big-O scalar,decoding complexity,explicit scalars,group testing schemes,nonadaptive group testing,Price-Scarlett's nonadaptive splitting,quickly-decodable group,Scarlett's fast binary splitting approach,uniformly random subset,vanishing error probability
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